Question 1: The sum of two numbers is and their difference is
. Find the numbers.
Answer:
Let the two numbers be
Add (i) and (ii)
Therefore
Hence the two numbers are
Question 2: Twice a number is equal to thrice the other number. If the sum of the numbers is , find the numbers.
Answer:
Let the two numbers are
Solving for
or
Therefore
Hence the two numbers are .
Question 3: Find two numbers such that twice the first added to thrice the second gives and twice the second added to thrice the first gives
.
Answer:
Let the numbers be
Solving for
Multiply i) by 2 and ii) by 3 and subtract ii) from i)
Substituting in i)
Hence the two numbers are
Question 4: Find two numbers which differ by and are such that four times the larger added to three times the smaller gives
.
Answer:
Let the numbers be
Solving by
Multiply i) by 4 and subtract ii) from i)
Calculating for
Hence the two numbers are
Question 5: The sum of two numbers is and the difference of their squares is
. Find the numbers.
Answer:
Let the two numbers be
Simplifying ii)
Solving for
Add i) and iii)
Substituting in i)
Hence the numbers are
Question 6: The sum of the digits of a two-digit number is . On adding
to the number, its digits are reversed. Find the number.
Answer:
Let the two digit numbers be
Simplifying ii)
Solving for
Add i) and iii)
Substituting in i)
Hence the numbers is
Question 7: Two digit number is three times the sum of its digits. lf is added to the number, its digits are reversed. Find the original number.
Answer:
Let the two digit numbers be
Simplifying i) and ii)
Solving for
Multiplying iv) by 7 and Subtract iv) from ii)
Hence
Therefore the numbers is
Question 8: A two-digit number is seven times the sum of its digits. If is subtracted from the number, its digits get interchanged. Find the number.
Answer:
Let the two digit number be
Solving for
Multiplying ii) by 3 and Subtract ii) from i)
Hence
Therefore the numbers is
Question 9: Find a fraction which reduces to when
is added to both its numerator and denominator; and reduces to
when
is added to both its numerator and denominator.
Answer:
Let the fraction be
Solving for
Multiplying i) by 5 and ii) by 3 and subtract ii) from i)
Hence
Therefore the fraction is
Question 10: On adding to the numerator of a fraction, it becomes
. Also, on adding
to the denominator of the original fraction, it becomes
. Find the original fraction.
Answer:
Let the fraction be
Solving for
Multiplying i) by 3 and ii) by 2 and subtract ii) from i)
Hence
Therefore the fraction is
Question 11: In a given fraction, if the numerator is multiplied by and the denominator is reduced by
, we get
. But, if the numerator of the given fraction is increased by
and the denominator is doubled, we get
. Find the fraction.
Answer:
Let the fraction be
Solving for
Multiplying ii) by 2 and subtract ii) from i
Hence
Therefore the fraction in
Question 12: years ago, a lady was thrice as old as her daughter.
years hence, the lady would be twice as old as her daughter. What are their present ages?
Answer:
Let the present age of lady
Let the Present age of Daughter
Solving for
Subtract ii) from i)
Hence
Therefore :
Lady’s Age
Daughter’s Age
Question 13: The sum of the ages of A and B is years. In
years’ time, the age of A will be twice the age of B. Find their present ages.
Answer:
Let A’s Age
Let B’s Age
Solving for
Subtract ii) from i)
or
Therefore
A’s Age
B’s Age
Question 14: A is years elder than B.
years ago A was four times as old as B. Find their present ages.
Answer:
Let the age of B
Hence A’s Age
Therefore
B’s Age
A’s Age
Question 15: Six years ago, the ages of Geeta and Seema were in the ratio . Nine years hence, their ages will be in the ratio
. Find their present ages.
Answer:
Let the age of Geeta
Let the age of Seema
Solving for
Multiplying i) by 7 and ii) by 4 and Subtract ii) from i)
Hence
Therefore
Geeta’s Age
Seema’s Age
Question 16: knives and
forks cost Rs.
, while
knives and,
forks together cost Rs.
. Find the cost of a knife and that of a fork.
Answer:
Let the cost of knives
Let the Cost of fork
Solving for
Multiplying i) by 3 and ii) 2
Hence
Hence Cost of :
Knive
Fork
Question 17: The cost of cups and
spoons is Rs.
, while the cost of
cups and
spoons is Rs.
. Find the cost of
cups and
spoons.
Answer:
Let the cost of Cup
Let the Cost of Spoon
Solve for
Multiply i) by 16 and ii) by 13 and subtract ii) from i)
Hence
Hence Cost of:
Cup
Spoon
Question 18: Rahul covered a distance of km in
hours, partly on bicycle at
kmph and partly on moped at
kmph. How much distance did he cover on moped?
Answer:
Total Distance
Total Time
Let the distance covered by cycle
Let the Distance covered by moped
Simplify
Hence Distance Covered by:
Cycle
Moped
Question 19: A boat can go km downstream in
hours and,
km upstream in
hours. Find i) the speed of the boat in still water (ii) the rate of the current.
Answer:
Let the Speed of boat in still water
Speed of Stream
Solve for , add i) and ii)
Speed of Stream
Question 20: The monthly incomes of A and B are in the ratio and their monthly savings are in the ratio
. If each spends Rs.
per month, find the monthly income of each.
Answer:
Let A’s Income
Let B’s Income
Substituting
Hence
Therefore :
A’s Income
B’s Income
Question 21: nuts and
bolts weigh
grams, while
nuts and
bolts weigh
grams. Find the weight of each nut and that of each bolt. How much do
nuts and
bolts weigh together?
Answer:
Let the Weight of Nut
Let the Height of Bolt
Solving for
Multiply i) by 8 and ii) by 6 and Subtract ii) from i)
Hence
Weight of:
Nut
Bolt
Therefore 3 Nuts and 3 Bolts will weight
Question 22: There are some girls in two classrooms, A and B. If girls are sent from room A to room B, the number of girls in both the rooms will become equal. If
girls are sent from room B to room A, then the number of girls in room A would be double the number of girls in room B. How many girls are there in each class room?
Answer:
Let No. of girls in classroom
Solving ,
Subtract ii) from i)
Hence
No. of Girls in Class Room:
Question 23: men and
boys can do a piece of work in
days, while
men and
boys can finish it in
days. How long would it take
man alone to do it?
Answer:
Suppose 1 man finished the work in days and 1 Boy finished the work in
days
There 1 man’s 1 day’s
And, 1 Boy’s 1 Day’s work
Now 4 men and 4 Boys finished the work in 3 days
Similarly 2 men and 5 boys finished in 4 days
Solving for
Multiply ii) by 2 and Subtract ii) from 2
or
Similarly
So one men can finished the work in
Question 24: A takes hours longer than B to walk
km. But, if A doubles his pace, he is ahead of B by
hour
minutes. Find the speeds of A and B.
Answer:
Let the Speed of A
Let the Speed of B
Time taken By A
Time Taken By B
If A Double him Race Time taken by A
Therefore
Hence
Question 25: If the length of a rectangle is reduced by m and breadth increased by
m, its area increases by
m2. If however, the length is increased by
m and breadth reduced by
m, then the area is reduced by
m2. Find the length and breadth of the rectangle.
Answer:
Let the Length of the rectangle
Let the Breadth of the rectangle
Solving for
From i)
Substituting in ii)
Hence
Therefore:
Length
Breadth
Sir, may I know the font you use.
Love that font 🙂
Cambria Math